I am driving through London in summer. There is no traffic. The sun is out, the roof is down, and a bus driver who has been edging aggressively close leans out of the window and says: "Madam, I like your car!"

Every part of this scenario sounds false. And yet, thanks to the Olympic summer, it was true: I had uncovered actual pleasure in cruising through the city. It might have had something to do with the transport-chaos scare stories that havecleared the roads of congestion quicker than a vat of Vicks. Personally, though, I put my happiness down to the 1968 Mercedes 280SL I was driving.

I had taken possession of this serene soft-top from Nigel at the Classic Car Club, which houses a batcave of beauties just off the Old Street roundabout. Nigel's stable stretches from vintage Rolls-Royces to modern sports cars; members pay a joining fee and an annual subscription to take them out. It's an (expensive) haven for petrolheads, but they are welcoming to the ingenue like me, who just wants to purr around in something stylish on the odd weekend.

Nigel led me past a Lotus Elan and an E Type to the more amenable touring car he had picked out for me. With its angular body and wide grille, this was a car that looked as smug as I would feel driving it.

I was given a few words on its quirks and asked to "take it slow". Oh-so-gently, I put my foot to the pedal. I went nowhere. I inched the pedal downwards. Still nowhere. Old cars: tsk. Nigel walked over. "You're in neutral."

In a vintage car, I needed a suitably old-fashioned destination. I headed for the South Downs, and for the Old Railway Station outside Petworth. This is a former station converted into a B&B, with the added charm that you can sleep in 1920s luxury in one of the lovingly restored Pullman carriages that grace its sidings. As I pulled up outside, a man in his 50s leaned out of what must once have been the ticket office window. "280SL!" he called out, the oddest greeting I've been given. "Automatic or manual?" "Automatic," I replied. "Ngh," he grunted. "Shame. Very rare to see a manual."

It transpired that Gudmund Olafsson, the Icelandic proprietor of the Old Railway Station, was more of a car enthusiast than a trainspotter. He talked me through my shining silver steed's good points (reliability, comfort) and bad (tricksy roof mechanism, rubbish as a getaway vehicle). Then I set out for a short tour around the countryside – a picnic on the Downs, some rubbernecking at the racecourse and a quick stop for a photo outside the Goodwood estate, spiritual home of classic cars. It was a showery afternoon, so I became adept at getting the roof on and off and secretly hoped this would catch people's attention. In fact, the car got far more glances when I wasn't in it. It sat there, all pleased with itself in car parks, attracting a swarm of interest – men too polite to touch, hovering over the chassis, peering through the window.

I decided I didn't mind being my car's sidekick. I was standing straighter. I was developing a demure smile. I even caught myself sashaying. This new sophistication was, of course, temporary – even a full membership of the Classic Car Club would only get me kitted out like this once a month. But it could be addictive.

The Classic Car Club has branches in London and New York (classiccarclub.co.uk). Membership costs from £1,555. The Old Railway Station (01798 342346, old-station.co.uk has doubles from £92 including breakfast